Interlayered composites with three types of cores were fabricated and tested. Quasi-static penetration tests (QSPTs), bending tests, and impact tests were conducted on the fabricated composites with carbon fiber epoxy laminate facings. Penetration test procedures were carried out until the composite was perforated and completely punctured. A 9 mm diameter rounded-tip punch was used; the diameter of the support hole was 45 mm. To determine the mechanical properties in the bending tests, three-point bending was carried out at a speed of 2 mm/min. Impact tests were also carried out using a Charpy impact test and a hammer with an energy of 2 J. Our findings indicate that the core material plays a crucial role in determining a composite’s mechanical behavior. Balsa cores offer the best properties in the QSPT test and bending strength and stiffness (57 MPa and 7.4 GPa, respectively), while Rohacell^® cores provide excellent impact resistance (12 kJ/m²). Nomex^® cores demonstrate high bending stiffness (5.3 GPa) but perform worse than Balsa. The choice of core material is application-dependent; Balsa cores are optimal for bending and point loads, and Rohacell^® cores are optimal for impact-dominated scenarios.